广义KdV方程与广义Burgers方程的精确解

利用试探函数法和直接积分法构造广义KdV方程与广义Burgers方程的新的精确解.     

一类非线性波方程整体解的存在性和不存在性

This paper deals with the existence and uniqueness of the global solution of the initial boundary value problem of a class of wave equation. In the meantime, it gives the sufficient conditions of blow-up of the solution for the problem in finite time.     

具奇异的非Newton渗流方程整体解存在性和渐进性

研究了一类奇异的非Newton多方渗流方程整体解存在性和渐进性，通过引进低能量函数的概念，证明了当初值uo(x)具有低能量时，其相应的解是整体存在的，且当t→∝时具有指数增长。     

Travelling Wave Solutions for Generalized Fisher Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１，２］，ＡｒｏｎｓｏｎａｎｄＷｅｉｎｂｅｒｇｅｒｈａｖｅｓｔｕｄｉｅｄｓｙｓｔｅｍａｔｉｃｌｙｔｈｅｓｃａｌａｒｎｏｎｌｉｎｅａｒｄｉｆｆｕ－ｓｉｏｎｅｑｕａｔｉｏｎｉｎｏｎｅｓｐａｃｅｖａｒｉａｂｌｅｕｔ＝ｕｘｘ＋φ（ｕ），（１．１）ｗｈｅｒｅｕ＝ｕ（ｘ，ｔ）ａｎｄφ（ｕ）ｉｓａｎｏｎｌｉｎｅａｒｆｕｎｃｔｉｏｎ．Ｅｑｕａｔｉｏｎ（１．１）ａｒｉｓｅｓｉｎｓｅｖｅｒａｌａｐｐｌｉｃａ－ｔｉｏｎｓ；Ｓｅｅ［１，２］ａｎｄ［３］ｆｏｒｉｎｆｏｒｍａｔｉｏｎａ…     

同伦分析法求解Burgers方程的初边值问题

采用同伦分析法求解了Burgers方程的一初边值问题,得到了它的近似解析解.在不同粘性系数情形下,对近似解与精确解进行了比较,发现在粘性系数不是非常小的情况下,用此方法得到的解析解与精确解符合地很好.     

非线性发展方程的变系数均衡作用法与变系数Burgers方程的解

利用非线性发展方程的变系数均衡作用法 ,借助计算机符号计算 ,求出变系数 Burgers方程的一种形式的解析解 .     

Large-Time Behavior of Periodic Solutions to Fractal Burgers Equation with Large Initial Data

The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutio...     

奇异特征值问题正解的全局结构

本文研究了奇异二阶微分方程特征值问题{y"(t)+μh(t)f(y(t))=0,0＜t＜1,αy(0)-βy'(0)=0,γy(1)+δy'(1)=0,其中α,γ＞0,β,δ≥0,h∈C((0,1),(0,+∞))且h在t=0和/或t=1处可能有奇性,f∈C([0,+∞),(0,+∞)),f(0)＞0和f∞=limf(s)/s=+∞.利用全局连续性定理、解的上下界和不动点指数相结合,给出了方程正解的存在性,多重性和不存在性,同时讨论了参数变化时解的变化趋势.     

(2+1)维Burgers方程新的复合解

In this paper, a new generalized compound Riccati equations rational expansion method （GCRERE） is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method is not only recover some known solutions, but also find some new and general complexiton solutions. Being concise and straightforward, it is applied to the （2＋1）-dimensional Burgers equation. As a result, eight families of new exact analytical solutions for this equation are found. The method can also be applied to other nonlinear partial differential equations.     

2+1维Ginzburg-Landau方程的精确波解

分析研究了一个具有三次增益效应和五次耗散项的2+1维Ginzburg-Landau方程.利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解.     

On the Decay Property of Solutions of Viscous Burgers Equation with Boundary Feedback

In this article, we will investigate the viscous Burgers equation with boundary feedback. The existence of the solution is proved by constructing a convergence sequence inductively. Moreover, the decay property of the solution is shown based on the maximum principle for nonlinear parabolic equations.     

Burgers方程的一类自相似解

利用李群理论中的伸缩变换群,将二阶非线性偏微分方程-Burgers方程化为一类Riccati方程和三类二阶非线性常微分方程,从而Riccati方程和这三类二阶非线性常微分方程给出了Burgers方程的自相似解的表现形式.     

一类拟线性波方程的整体光滑解

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxtt=β(uxn)x, where k>0 and βare real numbers, and n≥2 is an integer. We prove that for any T>0, the Cauchy problem admits a unique global smooth solution u ∈C∞((0, T); H∞(R))∩C ([0, T]; H2(R))∩C1([0, T]; L2(R)) under suitable assumptions on the initial data.     

The Global Smooth Solution for Landau-Lifshitz-Maxwell Equation Without Dissipation

In this paper, the global existence of a unique smooth solution for the Landau-Lifshitz-Maxwell equations of the ferromagnetic spin chain without dissipation in n (1 ≤ n ≤ 2) dimensions is established by using the viscosity elimination method.     

非线性Kirchhoff型波动方程全局吸引子的存在性

非线性Kirchhoff型波动方程描述了竖直方向上的波动.利用近似FaedoGalerkin的方法通过先验估计和一种新的验证紧性的方法(条件C)讨论了这类波动方程强解的全局吸引子.     

一类奇异双调和方程变号解的存在性

讨论了一类具有奇异系数的双调和问题其中N≥5:Ω是R~N中一有界光滑区域,0∈Ω,2~*(s)=2(N-s)/(n-4),0≤s≤4,20.利用一个新的环绕定理,讨论了该问题变号解的存在性.     

Distributed Control Problems for the Burgers Equation

In this work a distributed optimal control problem for time-dependent Burgers equation is analyzed. To solve the nonlinear control problems the augmented Lagrangian-SQP technique is used depending upon a second-order sufficient optimality condition. Numerical test examples are presented.     

分数阶耦合Burgers方程组的同伦摄动解

本文利用同伦摄动法求关于时间Burgers方程组的二阶近似解,为了说明此方法的有效性我们利用Maple 14软件作出了整数阶耦合Burgers方程组的近似解和精确解的图像.结果表明此方法计算量小,避免了对系数的复杂讨论过程并且得出的近似解精确度较高.     

一类耦合非线性波动方程全局解的存在性

利用微分不等式和解的延拓原理,研究了一类带非线性阻尼和源项的耦合非线性波动方程,通过分析方程中参数的关系,得到了全局解存在的一些新的充分条件.